Analysis of gene copy number changes in tumor phylogenetics

Jun Zhou, Yu Lin, Vaibhav Rajan, William Hoskins, Bing Feng, Jijun Tang

Evolution of cancer cells is characterized by large scale and rapid changes in the chromosomal  landscape. The fluorescence in situ hybridization (FISH) technique provides a way to measure the copy numbers of preselected genes in a group of cells and has been found to be a reliable source of data to model the evolution of tumor cells. Chowdhury et al. (Bioinformatics 29(13):189-98, 23; PLoS Comput Biol 10(7):1003740, 24) recently develop a computational model for tumor progression driven by gains and losses in cell count patterns obtained by FISH probes. Their model aims to find the rectilinear Steiner minimum tree (RSMT) (Chowdhury et al. in Bioinformatics 29(13):189-98, 23) and the duplication Steiner minimum tree (DSMT) (Chowdhury et al. in PLoS Comput Biol 10(7):1003740, 24) that describe the progression of FISH cell count patterns over its branches in a parsimonious manner. Both the RSMT and DSMT problems are NP-hard and heuristics are required to solve the problems efficiently. In this paper we propose two approaches to solve the RSMT problem, one inspired by iterative methods to address the "small phylogeny" problem (Sankoff et al. in J Mol Evol 7(2):133-49, 27; Blanchette et al. in Genome Inform 8:25-34, 28), and the other based on maximum parsimony phylogeny inference. We further show how to extend these heuristics to obtain solutions to the DSMT problem, that models large scale duplication events. Experimental results from both simulated and real tumor data show that our methods outperform previous heuristics (Chowdhury et al. in Bioinformatics 29(13):189-98, 23; Chowdhury et al. in PLoS Comput Biol 10(7):1003740, 24) in obtaining solutions to both RSMT and DSMT problems. The methods introduced here are able to provide more parsimony phylogenies compared to earlier ones which are consider better choices.